I you have a thousand applications for a move, which means a thousand ways to actually drop somebody you've worked your butt off and deserve congratuations. If they weren't passed to you who cares, all that matters is the attackers moves in and they're on the floor.

I´m not refering to different expressions of a single kata, but rather the different possible applications that can be done by a (sequence of) waza. I guess that's what you also describe in your question, by: ...maintain the structure and mechanics of the movement shown.These movements can be slightly alters so a different execution/application appears.

I have the idea that people who claim to 'know' three thousand applications actually mean, that by altering a uraken(backfist)- to a shuto(knifehand)-uchi(strike), they have a different application. Where in my vision, they have merely found a variation. The principle/structure/mechanics of the particular strike remain the same. Only the form of contact alters, which might have influence on the follow-up, but that's a different chapter.

I see kata like this:A kata is built up in sequences, made as a training aid. All of these sequences are open to variation. (Try for instance: stepping in a different direction; not during the complete kata, but by studying a sequence.) Some techniques are open to variation, because of similarities in structure and/or principle. (Tsuki can be many different hand forms, the same goes for uchi.)

Even consider hikite and soete; what are they in your* karate? *(Not specifically adressed at you Ronin1966, but in general.)

Does altering all shuto-uchi to uraken-uchi in a kata, make it a different kata?